Non-linear integral equations on unbounded domain with global polynomials

Ritu Nigam, Nilofar Nahid and Gnaneshwar Nelakanti

Applied Mathematics and Computation, 2024, vol. 471, issue C

Abstract: Solving Hammerstein - Fredholm integral equations on unbounded domains is challenging due to its domain of integration. Therefore, this paper discusses a numerical solution to the proposed problem using the Galerkin method, with low computational complexity and high convergence rates. In order to reduce the computational complexity, Laguerre polynomials are used as basis functions and to analyze the better convergence rates Kumar-Sloan (KS) approach has been applied. Further, the multi-Galerkin method with KS approach is used to improve the convergence results of Galerkin method. In addition, we have shown that the derivatives of the approximation solution converge to the corresponding derivatives of the exact solution with the same convergence rates as we attained for approximate solutions. Finally, numerical examples lend credibility to the presented theoretical framework.

Keywords: Superconvergence; Hammerstein - Fredholm integral equation; Galerkin and multi-Galerkin methods; Laguerre polynomials (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:471:y:2024:i:c:s0096300324000602

DOI: 10.1016/j.amc.2024.128588

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